By Topic

Upper bounds on trellis complexity of lattices

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Tarokh, Vahid ; AT&T Bell Labs., Murray Hill, NJ, USA ; Vardy, A.

Unlike block codes, n-dimensional lattices can have minimal trellis diagrams with an arbitrarily large number of states, branches, and paths. In particular, we show by a counterexample that there is no f(n), a function of n, such that all rational lattices of dimension n have a trellis with less than f(n) states. Nevertheless, using a theorem due to Hermite, we prove that every integral lattice Λ of dimension n has a trellis T, such that the total number of paths in T is upper-bounded by P(T)⩽n!(2/√3)n2(n-1/2)V(Λ) n-1 where V(n) is the volume of Λ. Furthermore, the number of states at time i in T is upper-bounded by |Si|⩽(2/√3)i2(n-1)V(Λ)2i2 n/. Although these bounds are seldom tight, these are the first known general upper bounds on trellis complexity of lattices

Published in:

Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 4 )